2005
DOI: 10.1016/j.geb.2004.03.002
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Compound voting and the Banzhaf index

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Cited by 29 publications
(26 citation statements)
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“…The first axiom is equivalent to the well-known transfer axiom of Dubey (1975), as remarked in Dubey et al (2005). Here we use a different name which reflects its content in a more direct manner.…”
Section: The Axiomsmentioning
confidence: 99%
“…The first axiom is equivalent to the well-known transfer axiom of Dubey (1975), as remarked in Dubey et al (2005). Here we use a different name which reflects its content in a more direct manner.…”
Section: The Axiomsmentioning
confidence: 99%
“…The transfer property says that if going from C ′ to C involves exactly the same increase in control as going from D ′ to D, then the power of each player should change by the same amount when going from C ′ to C as when going from D ′ to D. The transfer property is related to a property with the same name, used to characterize the Shapley value (Shapley, 1953) for (monotonic) simple games (Dubey, 1975). The form in which we present it is closely related to a version of the axiom discussed in Dubey et al (2005) and Einy and Haimanko (2011). The following lemma shows that TP is equivalent to a condition closely related to the original format of the transfer axiom as introduced in Dubey (1975).…”
Section: Constant-sum (Cs)mentioning
confidence: 99%
“…Thus, Bz is the normalized Banzhaf value (Banzhaf, 1965;Dubey et al, 2005). Define the power index ϕ by…”
Section: Constant-summentioning
confidence: 99%
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“…, g k in Equation 1 depend on disjoint subsets of variables). Under this assumption, Owen [1978] proved that the Penrose-Banzhaf index of a compound game can be recursively computed based on the following principle: the PB-index of a voter ℓ in a two-tiered compound game is equal to (the PB-index of ℓ in the first-tier game g i that he participates in) × (the PB-index of g i in the second-tier game) (see also Dubey, Einy and Haimanko [2005]). …”
Section: Pyramidal Structuresmentioning
confidence: 99%